1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ikadub [295]
3 years ago
8

Find the area of the region in the first quadrant bounded on the left by the ​y-​axis, below by the line y equals one third x co

mma above left by yequalsxplus​4, and above right by yequalsminusx squaredplus10.

Mathematics
1 answer:
bonufazy [111]3 years ago
8 0

Answer:

The bounded area  is: \frac{73}{6}\approx 12.17

Step-by-step explanation:

Let's start by plotting the functions that enclose the area, so we can find how to practically use integration. Please see attached image where the area in question has been highlighted in light green. The important points that define where the integrations should be performed are also identified with dots in darker green color. These two important points are: (2, 6) and (3, 1)

So we need to perform two separate integrals and add the appropriate areas at the end. The first integral is that of the difference of function y=x+4 minus function y=(1/3)x , and this integral should go from x = 0 to x = 2 (see the bottom left image with the area in red:

\int\limits^2_0 {x+4-\frac{x}{3} } \, dx =\int\limits^2_0 {\frac{2x}{3} +4} \, dx=\frac{4}{3} +8= \frac{28}{3}

The next integral is that of the difference between y=-x^2+10 and the bottom line defined by: y = (1/3) x. This integration is in between x = 2 and x = 3 (see bottom right image with the area in red:

\int\limits^3_2 {-x^2+10-\frac{x}{3} } \, dx =-9+30-\frac{3}{2} -(-\frac{8}{3} +20-\frac{2}{3} )=\frac{39}{2} -\frac{50}{3} =\frac{17}{6}

Now we need to add the two areas found in order to get the total area:

\frac{28}{3} +\frac{17}{6} =\frac{73}{6}\approx 12.17

You might be interested in
Can someone help me plz...
S_A_V [24]

Answer:

60 475

95 570

130 700

Step-by-step explanation:

subtract 95 from 60 then get that solution and add it to 95. then get 700 and subtract it from 130 then youll get 570 then subtract it again.

3 0
3 years ago
Assume f(x)=-2x+8 and g(x)=3x. what is the value of (g o f)(3)
Olin [163]

Answer:

6

Step-by-step explanation:

(g o f)(3) = g(f(3))

We can find f(3) using its formula with x=3:

f(3) = -2·3 +8 = -6 +8 = 2

Now, we can find g(2) using its formula with x=2:

g(2) = 3·2 = 6

So, the composition value is ...

(g o f)(3) = 6

7 0
3 years ago
What is the equation of the line that passes through the points (-7,-7) and (-7,4)
musickatia [10]

Answer:

Step-by-step explanation:

The equation of a line

y = mx + c

y - intercept point y

m - slope of the line

x - intercept point x.

c - intercept of the line

Step 1: find the slope

m = y2 - y1 / x2 - x1

Given two points

( -7 , -7) ( -7 , 4)

x1 = -7

y1 = -7

x2 = -7

y2 = 4

Insert the values into the equation

m = 4 - (-7) / -7 -(-7)

m = 4 + 7 / -7 + 7

m = 11/ 0

Step 2: sub any of the two points given into the equation

y= mx + c

y = 11/0x + c

(-7 ,4 )

x = -7

y = 4

4 = 11/0(-7) + c

4 = -77/0 +c

-77/0 is math error which means that the points are not correct

4 0
3 years ago
Find the percent of each number 60% of 250​
Nikolay [14]

Answer:

60% of 250​ is 150

7 0
3 years ago
Read 2 more answers
Translate the following into algebraic form: The difference of forty-seven and a number
JulsSmile [24]

Answer:

Number - 47

Step-by-step explanation:

difference means subtract

Number - 47

7 0
3 years ago
Other questions:
  • A country's population in 1990 was 48 million. In 1997 it was 51 million. Estimate the population in 2017 using the exponential
    9·1 answer
  • The dimensions of a rectangular garden were 4m by 5m. each dimension was increased b the same amount. the garden then had an are
    12·1 answer
  • I don't understand I need some help on it
    14·1 answer
  • Mark is six years older than his brother Sam. The sum of their ages is 30. Let a be Sam's age. Set up and solve an equation usin
    11·1 answer
  • Sarah knows that she needs $62000 for a 25% down payment on a house she can afford. she found an investment that earns 1.25% int
    15·1 answer
  • 3 children want to share 2 brownies so that everyone gets the same amount. How much brownie can each child have
    5·2 answers
  • Solve the inequality 24<5x-1
    7·2 answers
  • باستعمال log4 2=0.5 فإن قيمة log4 32 هي
    9·1 answer
  • 7m+9, for m=2.<br> What's the value of this equation
    12·1 answer
  • 5x - 3<br> BUNDYS<br> 21 - X<br> -<br> -<br> Q<br> S
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!